Internal problem ID [231]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-3 x \cos \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+4*y(x)=3*x*cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {3 \sin \left (2 x \right ) x^{2}}{8}-\frac {3 \sin \left (2 x \right )}{64}+\frac {3 x \cos \left (2 x \right )}{16} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 38
DSolve[y''[x]+4*y[x]==3*x*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{64} \left (24 x^2-3+64 c_2\right ) \sin (2 x)+\left (\frac {3 x}{16}+c_1\right ) \cos (2 x) \\ \end{align*}